Information and control: matching channels

Let 𝒳 serve as input alphabet and let 𝒴 serve as output alphabet. By adding dummy letters we can always assume that 𝒳⊂𝒴. The transmission of letters is ruled by a class 𝒲 of stochastic matrices with |𝒳| rows and |𝒴| columns. In addition to the sender and receiver, there is a third person (or device) called controller who decides which matrix W∈𝒲={(w(·|·|s):s∈S) shall govern the transmission of a letter by the sender. The controller knows which codeword the sender wants to transmit. The receiver has no knowledge about the actions of the controller. As code concept appropriate for this situation we introduce a matching code